Following [1]}, we augment the model with the latent variable \(u\)  such that the joint density of \(\left(\mathbf {\varepsilon },u\right)\)  is
\(f_{\mathbf {\varepsilon },u}\left(\mathbf {\varepsilon },u\right)=\underset{{\scriptstyle j=1}}{\overset{{\scriptstyle \infty }}{\sum }}\mathbb {I}\left(w_{j}>u\right)\text{logN}_{d}\left(\mathbf {\varepsilon }\left|\mathbf {m}_{j},\mathbf {\Sigma }_{j}\right.\right),\) 
